How many times in a day do the hour hand and the minute hand of a clock point opposite to each other?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 22
The hands point in opposite directions each time the minute hand gets 180° ahead of the hour hand, and then again after every further full lap it gains on it.
In 12 hours the minute hand goes round 12 times and the hour hand once, so the minute hand gains 11 laps
Each lap gained gives one position of the hands opposite each other: 11 times in 12 hours
In a day of 24 hours: \(11\times2=22\) times
It is 11, not 12, in each 12 hours because between 5 o’clock and 7 o’clock the hands are opposite only once, at 6:00.
Tip: In a day the hands coincide 22 times, are opposite 22 times and are at right angles 44 times.